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Strain Gauge Measurement – a Tutorial

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Strain Gauge Measurement – a Tutorial Application Note 078 Strain Gauge Measurement – A Tutorial What is Strain? Strain is the amount of deformation of a body due to an applied force. More specifically, strain (ε) is defined as the fractional change in length, as shown in Figure 1 below. Force Force D L ∆ ε = -------L L Figure 1. Definition of Strain Strain can be positive (tensile) or negative (compressive). Although dimensionless, strain is sometimes expressed in units such as in./in. or mm/mm. In practice, the magnitude of measured strain is very small. Therefore, strain is often expressed as microstrain (µε), which is ε × 10–6. When a bar is strained with a uniaxial force, as in Figure 1, a phenomenon known as Poisson Strain causes the girth of the bar, D, to contract in the transverse, or perpendicular, direction. The magnitude of this transverse contraction is a material property indicated by its Poisson's Ratio. The Poisson's Ratio ν of a material is defined as the negative ratio of the strain in the transverse direction (perpendicular to the force) to the strain in the axial direction (parallel to the ν ε ε force), or = – T/ . Poisson's Ratio for steel, for example, ranges from 0.25 to 0.3. The Strain Gauge While there are several methods of measuring strain, the most common is with a strain gauge, a device whose electrical resistance varies in proportion to the amount of strain in the device. For example, the piezoresistive strain gauge is a semiconductor device whose resistance varies nonlinearly with strain. The most widely used gauge, however, is the bonded metallic strain gauge. The metallic strain gauge consists of a very fine wire or, more commonly, metallic foil arranged in a grid pattern. The grid pattern maximizes the amount of metallic wire or foil subject to strain in the parallel direction (Figure 2). The cross sectional area of the grid is minimized to reduce the effect of shear strain and Poisson Strain. The grid is bonded to a thin backing, called the carrier, which is attached directly to the test specimen. Therefore, the strain expe- rienced by the test specimen is transferred directly to the strain gauge, which responds with a linear change in electrical resistance. Strain gauges are available commercially with nominal resistance values from 30 to 3000 Ω, with 120, 350, and 1000 Ω being the most common values. ————————————————— Product and company names are trademarks or trade names of their respective companies. 341023C-01 © Copyright 1998 National Instruments Corporation. All rights reserved. August 1998 alignment marks solder tabs active grid length carrier Figure 2. Bonded Metallic Strain Gauge It is very important that the strain gauge be properly mounted onto the test specimen so that the strain is accurately transferred from the test specimen, though the adhesive and strain gauge backing, to the foil itself. Manufacturers of strain gauges are the best source of information on proper mounting of strain gauges. A fundamental parameter of the strain gauge is its sensitivity to strain, expressed quantitatively as the gauge factor (GF). Gauge factor is defined as the ratio of fractional change in electrical resistance to the fractional change in length (strain): ∆ ⁄ ∆ ⁄ GF ==---------------RR- ---------------RR- ∆LL⁄ ε The Gauge Factor for metallic strain gauges is typically around 2. Ideally, we would like the resistance of the strain gauge to change only in response to applied strain. However, strain gauge material, as well as the specimen material to which the gauge is applied, will also respond to changes in tem- perature. Strain gauge manufacturers attempt to minimize sensitivity to temperature by processing the gauge material to compensate for the thermal expansion of the specimen material for which the gauge is intended. While compensated gauges reduce the thermal sensitivity, they do not totally remove it. For example, consider a gauge compensated for aluminum that has a temperature coefficient of 23 ppm/°C. With a nominal resistance of 1000 Ω, GF = 2, the equivalent strain error is still 11.5 µε/°C. Therefore, additional temperature compensation is important. Strain Gauge Measurement In practice, the strain measurements rarely involve quantities larger than a few millistrain (ε × 10–3). Therefore, to measure the strain requires accurate measurement of very small changes in resistance. For example, suppose a test specimen undergoes a substantial strain of 500 µε. A strain gauge with a gauge factor GF = 2 will exhibit a change in electrical resistance of only 2•(500 × 10–6) = 0.1%. For a 120 Ω gauge, this is a change of only 0.12 Ω. To measure such small changes in resistance, and compensate for the temperature sensitivity discussed in the previous section, strain gauges are almost always used in a bridge configuration with a voltage or current excitation source. The general Wheatstone bridge, illustrated below, consists of four resistive arms with an excitation voltage, VEX, that is applied across the bridge. 2 R 1 R 4 + V VO – EX – + R 2 R 3 Figure 3. Wheatstone Bridge The output voltage of the bridge, VO, will be equal to: R3 R 2 • VO = ------------------- –V------------------- EX R3 + R4 R 1 + R 2 From this equation, it is apparent that when R1/R2 = RG1/RG2, the voltage output VO will be zero. Under these condi- tions, the bridge is said to be balanced. Any change in resistance in any arm of the bridge will result in a nonzero output voltage. Therefore, if we replace R4 in Figure 3 with an active strain gauge, any changes in the strain gauge resistance will unbalance the bridge and produce a nonzero output voltage. If the nominal resistance of the strain gauge is designated ∆ ∆ • •ε as RG, then the strain-induced change in resistance, R, can be expressed as R = RG GF . Assuming that R1 = R2 and R3 = RG, the bridge equation above can be rewritten to express VO/VEX as a function of strain (see Figure 4). Note the presence of the 1/(1+GF•ε/2) term that indicates the nonlinearity of the quarter-bridge output with respect to strain. R 1 R G + R + V VO – EX – + R 2 R 3 V GF • ε 1 ---------O- =– ---------------- -------------------------- V 4 ε EX 1GF+ • --- 2 Figure 4. Quarter-Bridge Circuit By using two strain gauges in the bridge, the effect of temperature can be avoided. For example, Figure 5 illustrates a ∆ strain gauge configuration where one gauge is active (RG + R), and a second gauge is placed transverse to the applied strain. Therefore, the strain has little effect on the second gauge, called the dummy gauge. However, any changes in temperature will affect both gauges in the same way. Because the temperature changes are identical in the two gauges, the ratio of their resistance does not change, the voltage VO does not change, and the effects of the temperature change are minimized. 3 Dummy Gauge Active Gauge (RG, inactive) (RG + R) Figure 5. Use of Dummy Gauge to Eliminate Temperature Effects Alternatively, you can double the sensitivity of the bridge to strain by making both gauges active, although in different ∆ directions. For example, Figure 6 illustrates a bending beam application with one bridge mounted in tension (RG + R) ∆ and the other mounted in compression (RG – R). This half-bridge configuration, whose circuit diagram is also illus- trated in Figure 6, yields an output voltage that is linear and approximately doubles the output of the quarter-bridge circuit. Gauge in + tension F R R G R 1 (compression) ( R G + R ) + V VO – EX – + Gauge in compression – R 2 R G R ( R G – R ) (tension) V GF • ε ---------O- = – ---------------- VEX 2 Figure 6. Half-Bridge Circuit Finally, you can further increase the sensitivity of the circuit by making all four of the arms of the bridge active strain gauges, and mounting two gauges in tension and two gauges in compression. The full-bridge circuit is shown in Figure 7 below. R G – R R G + R + V VO – EX – + R G + R R G – R V ---------O-GF=–•ε VEX Figure 7. Full-Bridge Circuit The equations given here for the Wheatstone bridge circuits assume an initially balanced bridge that generates zero output when no strain is applied. In practice however, resistance tolerances and strain induced by gauge application will generate some initial offset voltage. This initial offset voltage is typically handled in two ways. First, you can use a special offset-nulling, or balancing, circuit to adjust the resistance in the bridge to rebalance the bridge to zero output. Alternatively, you can measure the initial unstrained output of the circuit and compensate in software. At the end of this application note, you will find equations for quarter, half, and full bridge circuits that express strain that take initial output voltages into account. These equations also include the effect of resistance in the lead wires connected to the gauges. 4 Lead Wire Resistance The figures and equations in the previous section ignore the resistance in the lead wires of the strain gauge. While ignoring the lead resistances may be beneficial to understanding the basics of strain gauge measurements, doing so in practice can be very dangerous. For example, consider the two-wire connection of a strain gauge shown in Figure 8a. Ω Suppose each lead wire connected to the strain gauge is 15 m long with lead resistance RL equal to 1 . Therefore, the lead resistance adds 2 Ω of resistance to that arm of the bridge. Besides adding an offset error, the lead resistance also desensitizes the output of the bridge. From the strain equations at the end of this application note, you can see that the amount of desensitization is quantified by the term (1 + RL/RG).
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